AFAIK it comes down to a mix of relatively recent population movements, the light touch of the millet system, and the Ottoman method of enforcing religious supremacy to explain why there aren’t so many Muslims/Turks in ex-Ottoman Europe as you’d expect.
Quite a lot of European Muslims fled or were forcibly extradited to Turkey during the final decades of the Ottoman Empire. The nationalistic revolutions were terrifying to these populations, many of whom were actively targeted by the revolutionaries. Many of the revolutionaries were not much better than armed thugs anyway, especially when not part of foreign Great Power meddling, meaning that Muslims were acceptable targets for disproportionate violence.
The millet system in the centuries before the age of nationalism hampered conversion effectively as it allowed the Orthodox and other Christian populations to continue practice of their faith without direct repression, which allowed their cultures to stay similar as well.
Lastly, the Ottoman methods of promoting Islam involved less of a focus on conversion and more of a focus on imperial superiority IMO. The devshirme system was arguably an effective propagandistic and political tool but hardly served to endear Islam to the nation’s Christian population.
As for European (Great Power) bias against the Ottoman Empire, you’re completely correct. During the 19th century the GPs came to feel that they were suffering the Ottomans to exist and began to play up the Empire’s flaws as part of their own imperial ambitions.
EDIT: There are significant populations of Muslims/Turks in certain narrow regions of the Balkans, especially in the southern parts. Some of these are under active cultural suppression. One example is in Western Thrace where they are stubbornly referred to as the “Muslim minority” despite being clearly specifically Turkish and have governmental interference in their religious leadership IIRC.